Could you elaborate? It sounds like you are talking more about challenges of distributed consensus (elections, raft). What I have in mind is distributed peering algorithms for decentralized networks. No consensus, elections, or quorum required. You may wish to run consensus algos on top of such networks but that's one layer up, if you will.
Byzantine in the context of unpermissioned networks is often explained as the sybil problem, which maps to the issues you mention.
Applying OP to this setting wouldn't mitigate that but I'm thinking it can be used as a framework to model and reason about these systems. Perhaps even prove certain properties (assuming some form of sybil resistance mechanism, I guess).